Taking \(\rho \approx 0.16\,\mathrm {fm}^{-3}\) , this gives approximately \(E_{0,\mathrm {(2D)}}^{\mathrm {kin},\phi _0\rightarrow \infty }(\rho )\approx 15.04\,\mathrm {MeV}\) . It is slightly large than the exact \(E_{\mathrm {F}}^{(2\mathrm {D})}\Lambda (2,C_0,\phi _0)\approx 13.69\,\mathrm {MeV}\)  if a finite high momentum cutoff \(\phi _0\approx 2.38\)  is used.
The FFG model prediction on the 2D kinetic EOS of SNM is simply \(k_{\mathrm {F}}^{(\mathrm {2D}),2}/4M=\pi \rho _2/4M\approx 9.60\,\mathrm {MeV}\)  where \(\rho _2=\rho ^{2/3}\) .
It is also very interesting to notice that if \(\epsilon =2\)  is applied in (REF ), then one obtains \(E_{0,\mathrm {(3D)}}^{\mathrm {kin},\phi _0\rightarrow \infty }(\rho )\approx 39.97\,\mathrm {MeV}\)  which is very close to the value of about 40.45 MeV [1]} if \(\phi _0\approx 2.38\)  and \(C_0\approx 0.161\)  are adopted in 3D.
Physically one can not extend the cutoff \(\phi _0\)  to infinity in conventional 3D situation. This is because above certain momentum the \(k^{-4}\)  form of the HMT in the single-nucleon momentum distribution is no longer reasonable again due to the higher-order correlations such as the three-nucleon interactions [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. In this case, other HMT forms in \(n_{\mathbf {k}}^0\)  should be necessarily considered.
